Journal of Optimization Theory and Applications

, Volume 155, Issue 1, pp 239–251

# On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs

• Shahid Ali
Article

## Abstract

In this paper, we introduce a new class of sets and a new class of functions called geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold. The concept of E-quasiconvex functions on R n is extended to geodesic E-quasiconvex functions on Riemannian manifold and some of its properties are investigated. Afterwards, we generalize the notion of epigraph called E-epigraph and discuss a characterization of geodesic E-convex functions in terms of its E-epigraph. Some properties of geodesic E-convex sets are also studied.

## Keywords

Geodesic E-convex sets Geodesic E-convex functions Geodesic E-quasiconvex function E-epigraphs Riemannian manifolds

## Notes

### Acknowledgements

The authors are highly thankful to anonymous referees and the editor for their valuable suggestions/comments which have contributed to the final preparation of the paper.

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